package com.wc.算法基础课.D第四讲数学知识.约数.约数个数;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

/**
 * @Author congge
 * @Date 2024/1/21 23:01
 * @description https://www.acwing.com/problem/content/872/
 */

public class Main {
    static FastReader sc = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    static int n, x;
    static int P = (int) 1e9 + 7;

    public static void main(String[] args) {
        n = sc.nextInt();
        HashMap<Integer, Integer> map = new HashMap<>();

        while (n-- > 0) {
            x = sc.nextInt();
            for (int i = 2; i <= x / i; i++) {
                if (x % i == 0) {
                    int t = 0;
                    while (x % i == 0) {
                        t++;
                        x /= i;
                    }
                    map.put(i, map.getOrDefault(i, 0) + t);
                }
            }
            if (x > 1) {
                map.put(x, map.getOrDefault(x, 0) + 1);
            }
        }
        long res = 1;
        for (Map.Entry<Integer, Integer> kv : map.entrySet()) {
            res = res * (kv.getValue() + 1) % P;
        }
        out.println(res);
        out.flush();
    }
}

class FastReader {
    StringTokenizer st;
    BufferedReader br;

    FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    String nextLine() {
        String s = "";
        try {
            s = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return s;
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    // 是否由下一个
    boolean hasNext() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                String line = br.readLine();
                if (line == null)
                    return false;
                st = new StringTokenizer(line);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return true;
    }
}
